Mobile robots can be broadly categorized as statically stable, e.g., stable when unpowered, and dynamically stable, e.g., stable only when powered. Statically stable robots generally have at least three wheels. A significant but frequently overlooked problem is that statically stable wheeled mobile robots can easily become unstable. If the center of gravity is too high, or the robot accelerates/decelerates too rapidly, or is on a sloping surface, or is pushed too hard, the robot can tip over. Thus, statically stable wheeled robots tend to have low centers of gravity and large bases. However, short, wheeled robots having large bases do not interact well with humans and have trouble maneuvering in environments that are crowded or cluttered.
A ball-balancing robot, or BBR, also known as a “ballbot”, is a dynamically-stable mobile robot designed to balance on a single spherical wheel (i.e., a ball). Through its single contact point with the ground, a ballbot is omnidirectional and thus exceptionally agile, maneuverable and organic in motion compared to other ground vehicles. Its dynamic stability enables improved navigability in narrow, crowded and dynamic environments. The BBR works on the same principle as that of an inverted pendulum. It forms an underactuated system, in which there are more degrees of freedom (DOF) than there are independent control inputs. The ball is directly controlled using actuators, whereas the body has no direct control. The body is kept upright about its unstable equilibrium point by controlling the ball, much like the control of an inverted pendulum. This leads to limited but perpetual position displacements of the BBR. The counter-intuitive aspect of the BBR motion is that in order to move forward, the body has to lean forward and in order to lean forward, the ball must roll backwards. All these characteristics make planning to achieve desired motions for the ballbot a challenging task. In order to achieve a forward straight line motion, the ballbot has to lean forward to accelerate and lean backward to decelerate. Further, the ballbot must lean into curves in order to compensate for centripetal forces, which results in elegant and graceful motions.
BBRs exhibit rich 3D dynamics and are capable of fluid and graceful motion. Early research on BBRs appeared around 2006. The first successful ballbot was developed by Hollis and co-workers at Carnegie Mellon University (CMU), and is described in U.S. Pat. No. 7,847,504, which is incorporated herein by reference. This robot is also described by T. B. Lauwers, et al. in “A Dynamically Stable Single-Wheeled Mobile Robot with Inverse Mouse-Ball Drive”, Proc. of the 2006 IEEE Int'l Conf. on Robotics and Automation, Orlando, Fla., May 2006, pp. 2884-2889. The described robot applies two roller bars to drive the ball in any direction but does not accommodate the ability to spin in place as the rollers used in the prior art act in interference of one another.
The omniwheel drive mechanism described by Wu et al. in U.S. Pat. No. 8,485,938, the disclosure of which is incorporated herein by reference, utilizes sets of guide rollers on axles that are arranged perpendicular to each other, i.e., 90° apart, so that the guide rollers contact the surface of the spherical wheel oriented to effectively define a cross pattern on the wheel that intersects a line corresponding to the wheel's north pole. The vertical positioning of the guide rollers limits the ability to spin in place.
Other ballbots have been described in the literature, including one developed by M. Kumagai and T. Ochiai, “Development of a Robot Balancing on a Ball”, Int'l Conf. on Control, Automation and Systems 2008, Oct. 14-17, 2008, Seoul, Korea, pp. 433-438. This robot uses a single angle in engaging the ball while maintaining the drive motors vertically. This arrangement limits the mobility of the robot, and makes it difficult to spin in place. (The disclosures of both identified publications are incorporated herein by reference.)
To date, most BBR research has focused on human-scale designs, ball-balancing transportation vehicles, and knee-high to waist-high designs. A smaller scale robot, such as would be useful for entertainment, i.e., toys, service, education and research, is referred to as a “micro ball-balancing robot”, or “MBBR”, pronounced “Ember.”
There are significant challenges and limitations to contend with when attempting to miniaturize a BBR. Tolerances become more stringent and cross-sectional areas decrease, lowering the yield strength of mechanical components. Scaling down the characteristic length scale (l) of a given design generally reduces the volume and mass of the design by l3; on a BBR, this significantly reduces the normal force between the omniwheels and the ball, creating problems with slip. Simultaneously, the time scale of the non-minimum-phase inverted-pendulum dynamics of a BBR is √{square root over (l/g)}, so as l is reduced, the time scale decreases, and the actuators must respond more quickly, further exacerbating the slip problem. In extreme cases, the drive wheels may even lose contact with the ball completely for short periods of time.
Earlier work on BBRs fall into two main categories: those driven by an inverse mouseball mechanism, and those driven by three omniwheels. In principle, neither category presents obvious barriers to miniaturization. The inverse mouseball mechanism relies on two perpendicular rollers that roll along the equator of the ball. A small, low-friction bearing is used at the top of the ball to support the weight of the upper body. Spring-loaded idler wheels at opposite points along the equator press the rollers against the ball to create enough friction to eliminate slip between the rollers and the ball. This allows the rollers to actuate the ball in the two horizontal directions independently.
There are two key problems with MBBRs driven by an inverse mouseball mechanism. The first was contamination. During testing, dirt and rubber particles can build up on the support bearing, idler wheels, and drive rollers. This increases friction and degrades performance to the point of failure. For large BBRs, the torques and forces involved are greater in magnitude, and tolerances are relaxed, so a thin layer of dirt has little effect on performance. However, for an MBBR, dirt buildup on the rotating components can be a critical point of failure.
A second problem encountered was the ball being pushed out of the socket during maneuvers. The rollers transmit torque to the ball by applying a friction force along the ball's equator. Depending on the direction of rotation, this force tends either to push the ball further into the socket, or to pull the ball away from the socket. The only force preventing the ball from leaving the socket is the weight of the robot itself. Since MBBRs have reduced mass, their weight is generally insufficient to keep the ball in the socket. Even if the ball does not leave the socket, the design suffers from asymmetric friction. As the roller actuates the ball in one direction, the ball is forced into the socket, increasing both the normal force and the friction at the top support bearing. When actuating the ball in the opposite direction, the friction at the top support bearing is reduced. Additionally, the inverse mouseball mechanism does not control the yaw of the robot about its vertical axis, so additional actuators would be needed to make the robot face in a desired direction. Given its significant problems, an inverse mouseball mechanism cannot be considered a viable choice for an MBBR.